Article: Q28249
Product(s): See article
Version(s): 1.00 1.01 1.02 2.00 2.01 3.00 4.00 4.00b 4.50
Operating System(s): MS-DOS
Keyword(s): ENDUSER | B_BasicCom B_GWBasicI B_BasicInt B_MQuickB B_BBasic | mspl13_basic
Last Modified: 10-JAN-1991
From the BASIC functions LOG, COS, SIN, TAN, SGN, EXP, and SQR, you
can derive the other transcendental functions as shown below.
The following trigonometric and mathematical functions that are not
intrinsic to BASIC can be calculated as shown:
Function BASIC Equivalent
-------- ----------------
Secant SEC(X) = 1/COS(X)
Cosecant CSC(X) = 1/SIN(X)
Cotangent COT(X) = 1/TAN(X)
Inverse Sine ARCSIN(X) = ATN(X/SQR(1-X*X))
Inverse Cosine ARCCOS(X) = -ATN(X/SQR(X*X-1)) + Pi/2
Inverse Secant ARCSEC(X) = ATN(X/SQR(X*X-1)) + (SGN(X)-1) * Pi/2
Inverse Cosecant ARCCSC(X) = ATN(1/SQR(X*X-1)) + (SGN(X)-1) * Pi/2
Inverse Cotangent ARCCOT(X) = -ATN(X) + Pi/2
Hyperbolic Sine SINH(X) = (EXP(X) - EXP(-X))/2
Hyperbolic Cosine CACHE(X) = (EXP(X) + EXP(-X))/2
Hyperbolic Tangent TANH(X) = (EXP(X) - EXP(-X))/(EXP(X) + EXP(-X))
Hyperbolic Secant SECH(X) = 2/(EXP(X) + EXP(-X))
Hyperbolic Cosecant CSCH(X) = 2/(EXP(X) - EXP(-X))
Hyperbolic Cotangent COTH(X) = EXP(-X)/(EXP(X) - EXP(-X)) * 2 + 1
Inverse Hyperbolic Sine ARCSINH(X) = LOG(X + SQR(X*X+1))
Inverse Hyperbolic Cos ARCCOSH(X) = LOG(X + SQR(X*X-1))
Inverse Hyperbolic Tan ARCCTANH(X) = LOG((1 + X)/(1 - X)) / 2
Inverse Hyperbolic CSC ARCCSCH(X) = LOG((SGN(X)*SQR(X*X+1)+1)/X)
Inverse Hyperbolic Sec ARCSECH(X) = LOG((SQR(1-X*X)+1) / X)
Inverse Hyperbolic Cot ARCCOTH(X) = LOG((X+1)/(X-1)) / 2
The above general formulas may be used in Microsoft BASIC or any other
language. Note that the constant Pi has the following approximate
value:
Pi# = 3.14159265359
Pi# = 4.0# * ATN(1.0#)
The above information applies to most Microsoft BASIC products,
including the following:
1. Microsoft QuickBASIC versions 1.00, 1.01, 1.02, 2.00, 2.01,
3.00, 4.00, 4.00b, and 4.50 for the IBM PC
2. Microsoft BASIC Compiler versions 6.00 and 6.00b for MS-DOS and
MS OS/2, and Microsoft BASIC Compiler versions 5.35 and 5.36 for
MS-DOS
3. Microsoft GW-BASIC Interpreter versions 3.20, 3.22, and 3.23
4. Microsoft BASIC Interpreter versions 1.00, 1.01, 2.00, 2.10,
and 3.00 for the Apple Macintosh
5. Microsoft BASIC Compiler version 1.00 for the Apple Macintosh
6. Microsoft QuickBASIC version 1.00 for the Apple Macintosh
7. Microsoft BASIC Professional Development System (PDS) versions 7.00
and 7.10 for MS-DOS and MS OS/2
8. Microsoft Business BASIC Compiler versions 1.00 and 1.10 for MS-DOS
(discontinued product)
9. Microsoft BASIC Interpreter (BASIC86.EXE) version 5.28 for MS-DOS